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A comparison between (strongly) distributive sentences in two typologically different languages, i.e. Romanian and Chinese is proposed. It is argued that the same factors, namely the inherent properties of the quantifiers more than the c-command relations obtaining between them constrain the possible interpretations of distributive sentences. The importance of the two factors is relatively different: in Romanian, the semantic factor cannot be superseded by the configurational one, whereas in Chinese c-command is at least equally important, thus partially confirming the isomorphism thesis.

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We assume the reader is familiar with basic notions of lattice theory and of universal algebra. A small portion of [ 9 ] is sufficient as a prerequisite. A lattice is distributive if and only if it satisfies the identity α ( β + γ ) ≤ α β + γ . It

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distributivity in pluralities . In A. K. Biller , E. Y. Chung and A. E. Kimball (eds.) Proceedings of the 36th Annual Boston University Conference on Language Development (BUCLD) . Somerville, MA : Cascadilla Press . 387 – 399 . Schlottmann

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It is shown that, if two bounded distributive lattices satisfy the join-infinite distributive law (JID), then their coproduct also satisfies this law. In 1986, Yaqub proved that generalized Post algebras with a finite lattice of constants satisfy JID, and stated that, in general, it is not known whether a generalized Post algebra satisfies JID when its lattice of constants satisfies JID. In this note, the statement is proved.

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. C ., and Koh , K. M . On the length of the lattice of sublattices of a finite distributive lattice . Algebra Universalis 15 , 2 ( 1982 ), 233 – 241 . [6] Chen , C. C ., Koh , K. M ., and Teo , K. L . On the sublattice-lattice of a

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The relationship between absolute retracts, injectives and equationally compact algebras in finitely generated congruence distributive varieties with 1- element subalgebras is considered and several characterization theorems are proven. Amongst others, we prove that the absolute retracts in such a variety are precisely the injectives in the amalgamation class and that every equationally compact reduced power of a finite absolute retract is an absolute retract. We also show that any elementary amalgamation class is Horn if and only if it is closed under finite direct products.

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LetS be a 0-distributive semilattice and be its minimal spectrum. It is shown that is Hausdorff. The compactness of has been characterized in several ways. A representation theorem (like Stone's theorem for Boolean algebras) for disjunctive, 0-distributive semilattices is obtained.

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Abstract  

We prove that the tolerance lattice TolA of an algebra A from a congruence modular variety V is 0-1 modular and satisfies the general disjointness property. If V is congruence distributive, then the lattice Tol A is pseudocomplemented. If V admits a majority term, then Tol A is 0-modular.

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